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Quantum separability criteria based on realignment moments

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Abstract

Quantum entanglement is the core resource in quantum information processing and quantum computing. It is a significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented by Elben et al. (Phys Rev Lett 125:200501, 2020) based on the first three partially transposed (PT) moments of density matrices. Then, Yu et al. (Phys Rev Lett 127:060504, 2021) proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant Nos. 12126314, 12126351, 11861031, 12075159 and 12171044, Beijing Natural Science Foundation (Z190005), the Hainan Provincial Natural Science Foundation of China under Grant No.121RC539, and Academy for Multidisciplinary Studies, Capital Normal University. This project is also supported by the specific research fund of The Innovation Platform for Academicians of Hainan Province under Grant No. YSPTZX202215.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hainan Normal University, Haikou, 571158, China

    Tinggui Zhang & Shao-Ming Fei

  2. College of Sciences, Shanghai University, Shanghai, 200444, China

    Tinggui Zhang & Naihuan Jing

  3. Department of Mathematics, North Carolina State University, Raleigh, USA

    Naihuan Jing

  4. School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China

    Shao-Ming Fei

  5. Max-Planck-Institute for Mathematics in the Sciences, 04103, Leipzig, Germany

    Shao-Ming Fei

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  1. Tinggui Zhang
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  2. Naihuan Jing
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Correspondence to Tinggui Zhang.

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Zhang, T., Jing, N. & Fei, SM. Quantum separability criteria based on realignment moments. Quantum Inf Process 21, 276 (2022). https://doi.org/10.1007/s11128-022-03630-6

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